How do you write an equation in slope-intercept form of the line that passes through the points (-7,-3) and (-12,5)?
1 Answer
Explanation:
The equation of a line in
#color(blue)"slope-intercept form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the slope and b, the y-intercept.We have to find m and b.
To find m, use the
#color(blue)"gradient formula"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#
where# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"# The 2 points here are (-7 ,-3) and (-12 ,5)
let
# (x_1,y_1)=(-7,-3)" and " (x_2,y_2)=(-12,5)#
#rArrm=(5-(-3))/(-12-(-7))=8/(-5)=-8/5# We can now write the partial equation
#y=-8/5x+b# To find b, substitute either of the 2 given points into the
partial equationChoosing (-12 ,5) that is x = - 12 and y = 5
#5=(-8/5xx-12)+b#
#rArr5=96/5+brArrb=5-96/5=25/5-96/5=-71/5#
#rArry=-8/5x-71/5" is the equation of the line"#
